arXiv subjects

Xiaobai Zhu

Publications and source records attributed to Xiaobai Zhu.

4 recordsLinked to original sources

arXiv2026

A Tale of Two Pathways to Gompertz Mortality: Reliability and Vitality from an Actuarial Perspective

This paper studies two mechanistic explanations for human mortality by examining reliability theory and vitality modelling through a unified actuarial perspective. While the two approaches arise from different ageing mechanisms, we show that both can naturally generate the Gompertz law under suitable assumptions and can be extended to produce the Makeham law and late-life mortality plateaus. Using Canadian mortality data, we investigate the empirical behaviour of each approach and highlight the roles of heterogeneity, extrinsic risk, and stochastic randomness. Furthermore, we develop parallel definitions of biological age under both approaches and analyse how subjective survival beliefs emerge from misspecified parameters. Our comparison of these two approaches provides actuarial insights into the natural foundations of Gompertz mortality and the interpretation of ageing, frailty and death.

stat.OT↗

arXiv2026

Mortality Heterogeneity and Actuarial Fairness in China's Notional Defined Contribution Pension System

We study actuarial fairness in China's notional defined contribution (NDC) pension system when mortality differs across income groups. Under current rules, individual account balances are converted into monthly benefits using an official annuity divisor that depends only on retirement age. We develop a mortality-differentiated Lee-Carter framework with group-specific baseline mortality schedules and a common period effect, estimated by combining national mortality data for 1994-2020 with CHARLS subgroup data for 2011-2020. To model cross-group mortality parsimoniously under limited data, we parameterize the baseline schedules using Hermite splines. Applying the model to China's NDC system, we find substantial actuarial unfairness in the current age-only divisor. The subsidy rises monotonically with income, implying both an aggregate actuarial shortfall and a reverse transfer from poorer to richer retirees. We then compare four implementable income-dependent annuitization rules, ranging from a simple bracket design to marginal-rule alternatives, and show that all substantially reduce the reverse transfer.

q-fin.RM↗

arXiv2024

A new paradigm of mortality modeling via individual vitality dynamics

The significance of mortality modeling extends across multiple research areas, ranging from life insurance valuation to optimal lifetime decision-making. Existing approaches, such as mortality laws and factor-based models, often fall short in capturing the complexity of individual mortality, hindering their ability to address specific research needs. To overcome these limitations, this paper introduces a novel approach to mortality modeling centered on the dynamics of individual vitality. A four-component framework is developed to account for initial conditions, natural aging processes, stochastic fluctuations, and accidental events over an individual's lifetime. We demonstrate the framework's analytical capabilities across various settings and explore its practical implications in solving life insurance problems and deriving optimal lifetime decisions. Our results show that the proposed framework not only encompasses existing mortality models but also provides individualized mortality outcomes and offers an intuitive explanation for survival biases.

stat.AP↗

arXiv2017

Valuation of a Bermudan DB underpin hybrid pension benefit

In this paper we consider three types of embedded options in pension benefit design. The first is the Florida second election (FSE) option, offered to public employees in the state of Florida in 2002. Employees were given the option to convert from a defined contribution (DC) plan to a defined benefit (DB) plan at a time of their choosing. The cost of the switch was assessed in terms of the ABO (Accrued Benefit Obligation), which is the expected present value of the accrued DB pension at the time of the switch. If the ABO was greater than the DC account, the employee was required to fund the difference. The second is the DB Underpin option, also known as a floor offset, under which the employee participates in a DC plan, but with a guaranteed minimum benefit based on a traditional DB formula. The third option can be considered a variation on each of the first two. We remove the requirement from the FSE option for employees to fund any shortfall at the switching date. The resulting option is very similar to the DB underpin, but with the possibility of early exercise. Since we assume that exercise is only permitted at discrete, annual intervals, this option is a Bermudan variation on the DB Underpin. We adopt an arbitrage-free pricing methodology to value the option. We analyse and value the optimal switching strategy for the employee by constructing an exercise frontier, and illustrate numerically the difference between the FSE, DB Underpin and Bermudan DB Underpin options.

q-fin.PR↗